引力:基础与前沿

内容概要

(印)帕德马纳班：印度IUCAA教授。

书籍目录

List of exercises

List of projects

Preface

How to use this book

1 Special relativity

1.1 Introduction

1.2 The principles of special relativity

1.3 Transformation of coordinates and velocities

1.3.1 Lorentz transformation

1.3.2 Transformation of velocities

1.3.3 Lorentz boost in an arbitrary direction

1.4 Four—vectors

1.4.1 Four—velocity and acceleration

1.5 Tensors

1.6 Tensors as geometrical objects

1.7 Volume and surface integrals in four dimensions

1.8 Particle dynamics

1.9 The distribution function and its moments

1.10 The Lorentz group and Pauli matrices

2 Scalar and electromagic fields in special relativity

2.1 Introduction

2.2 External fields of force

2.3 Classical scalar field

2.3.1 Dynamics of a particle interacting with a scalarfield

2.3.2 Action and dynamics of the scalar field

2.3.3 Energy—momentum tensor for the scalar field

2.3.4 Free field and the wave solutions

2.3.5 Why does the scalar field lead to an attractiveforce？

2.4 Electromagic field

2.4.1 Charged particle in an electromagic field

2.4.2 Lorentz transformation of electric and magicfields

2.4.3 Current vector

2.5 Motion in the Coulomb field

2.6 Motion in a constant electric field

2.7 Action principle for the vector field

2.8 Maxwell's equations

2.9 Energy and momentum of the electromagic field

2.10 Radiation from an accelerated charge

2.11 Larmor formula and radiation reaction

3 Gravity and spaeetime geometry： the inescapable connection

3.1 Introduction

3.2 Field theoretic approaches to gravity

3.3 Gravity as a scalar field

3.4 Second rank tensor theory of gravity

3.5 The principle of equivalence and the geometricaldescription of gravity

3.5.1 Uniformly accelerated observer

3.5.2 Gravity and the flow of time

4 Metric tensor， geodesics and covariant derivative

4.1 Introduction

4.2 Metric tensor and gravity

4.3 Tensor algebra in curved spacetime

4.4 Volume and surface integrals

4.5 Geodesic curves

4.5.1 Properties of geodesic curves

4.5.2 Affine parameter and null geodesics

4.6 Covariant derivative

4.6.1 Geometrical interpretation of the covariantderivative

4.6.2 Manipulation of covariant derivatives

4.7 Parallel transport

4.8 Lie transport and Killing vectors

4.9 Fermi—Walker transport

5 Curvature of spaeetime

5.1 Introduction

5.2 Three perspectives on the spacetimecurvature

5.2.1 Parallel transport around a closed curve

5.2.2 Non—mutativity of covariant derivatives

5.2.3 Tidal acceleration produced by gravity

5.3 Properties of the curvature tensor

5.3.1 Algebraic properties

5.3.2 Bianchi identity

5.3.3 Ricci tensor， Weyl tensor and conformal transformations

5.4 Physics in curved spacetime

5.4.1 Particles and photons in curved spacetime

5.4.2 Ideal fluid in curved spacetime

5.4.3 Classical field theory in curved spacetime

5.4.4 Geometrical optics in curved spacetime

5.5 Geodesic congruence and Raychaudhuri's equation

5.5.1 Timelike congruence

5.5.2 Null congruence

5.5.3 Integration on null surfaces

5.6 Classification of spacetime curvature

5.6.1 Curvature in two dimensions

5.6.2 Curvature in three dimensions

5.6.3 Curvature in four dimensions

6 Einstein's field equations and gravitational dynamics

6.1 Introduction

6.2 Action and gravitational field equations

6.2.1 Properties of the gravitational action

6.2.2 Variation of the gravitational action

6.2.3 A digression on an alternative form of action functional

6.2.4 Variation of the matter action

6.2.5 Gravitational field equations

6.3 General properties of gravitational field equations

6.4 The weak field limit of gravity

6.4.1 Metric of a stationary source in linearized theory

6.4.2 Metric of a light beam in linearized theory

6.5 Gravitational energy—momentum pseudo—tensor

7 Spherically symmetric geometry

7.1 Introduction

7.2 Metric of a spherically symmetric spacetime

7.2.1 Static geometry and Birkoff's theorem

7.2.2 Interior solution to the Schwarzschild metric

7.2.3 Embedding diagrams to visualize geometry

7.3 Vaidya metric of a radiating source

7.4 Orbits in the Schwarzschild metric

7.4.1 Precession of the perihelion

7.4.2 Deflection of an ultra—relativistic particle

7.4.3 Precession of a gyroscope

7.5 Effective potentialfor orbits in the Schwarzschild metric

7.6 Gravitational collapse of a dust sphere

8 Black holes

8.1 Introduction

8.2 Horizons in spherically symmetric metrics

8.3 Kruskal—Szekeres coordinates

8.3.1 Radial infall in different coordinates

8.3.2 General properties of maximal extension

8.4 Penrose—Carter diagrams

8.5 Rotating black holes and the Kerr metric

8.5.1 Event horizon and infinite redshift surface

8.5.2 Static limit

8.5.3 Penrose process and the area of the event horizon

8.5.4 Particle orbits in the Kerr metric

8.6 Super—radiance in Kerr geometry

8.7 Horizons as null surfaces

9 Gravitational waves

9.1 Introduction

9.2 Propagating modes of gravity

9.3 Gravitational waves in a fiat spacetime background

9.3.1 Effect of the gravitational wave on a system of particles

9.4 Propagation of gravitational waves in the curved spacetime

9.5 Energy and momentum of the gravitational wave

9.6 Generation of gravitational waves

9.6.1 Quadrupole formula for the gravitational radiation

9.6.2 Back reaction due to the emission of gravitational waves

9.7 General relativistic effects in binary systems

9.7.1 Gravitational radiation from binary pulsars

9.7.2 Observational aspects of binary pulsars

9.7.3 Gravitational radiation from coalescing binaries

10 Relativistic cosmology

10.1 Introduction

10.2 The Friedmann spacetime

10.3 Kinematics of the Friedmann model

10.3.1 The redshifting of the momentum

10.3.2 Distribution functions for particles and photons

10.3.3 Measures of distance

……

11 Differential forms and exterior calculus

12 Hamiltonian structure of general relativity

13 Evolution of cosmological perturbations

14 Quantum field theory in curved snacetime

15 Gravity in higher and lower dimensions

16 Gravity as an emergent phenomenon

作者简介

《Gravitation：Foundations and Frontiers引力——基础与前沿（影印版）》是从剑桥大学出版社引进的影印版图书。引力是自然界已知的基本相互作用之一。从牛顿的万有引力理论，到爱因斯坦的广义相对论，引力的研究不断革命性地改变着人类对于客观世界的认识。我们对于宇宙的研究，也是以引力理论为基础。本书系统、全面地讲述了当代引力理论，而且深入地探讨了最前沿的各种课题。无论是在这一领域工作的科研工作者和研究生，还是其他方向的，对于物理学有兴趣的读者，都不应错过这本佳作。

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